TSTP Solution File: SET678+3 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET678+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:09 EDT 2024
% Result : Theorem 1.41s 0.60s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 159 ( 16 unt; 0 def)
% Number of atoms : 496 ( 35 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 568 ( 231 ~; 238 |; 30 &)
% ( 23 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 235 ( 230 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> compose(identity_relation_of(B),C) = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(range_of(C),B)
=> compose(C,identity_relation_of(B)) = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),binary_relation_type) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
? [B] : ilf_type(B,binary_relation_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( compose(C,identity_relation_of(B)) = C
& compose(identity_relation_of(B),C) = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( compose(C,identity_relation_of(B)) = C
& compose(identity_relation_of(B),C) = C ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ~ subset(domain_of(C),B)
| compose(identity_relation_of(B),C) = C ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f42,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ subset(domain_of(X1),X0)
| compose(identity_relation_of(X0),X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ~ subset(range_of(C),B)
| compose(C,identity_relation_of(B)) = C ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f44,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ subset(range_of(X1),X0)
| compose(X1,identity_relation_of(X0)) = X1 ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f59,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ilf_type(identity_relation_of(B),binary_relation_type) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f60,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(identity_relation_of(X0),binary_relation_type) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f62,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(C,identity_relation_of_type(B))
| ilf_type(C,relation_type(B,B)) )
& ( ilf_type(C,identity_relation_of_type(B))
| ~ ilf_type(C,relation_type(B,B)) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ilf_type(X1,relation_type(X0,X0)) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f83,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f84,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ ilf_type(B,binary_relation_type)
| ( relation_like(B)
& ilf_type(B,set_type) ) )
& ( ilf_type(B,binary_relation_type)
| ~ relation_like(B)
| ~ ilf_type(B,set_type) ) ) ),
inference(NNF_transformation,[status(esa)],[f83]) ).
fof(f87,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f84]) ).
fof(f88,plain,
ilf_type(sk0_4,binary_relation_type),
inference(skolemization,[status(esa)],[f14]) ).
fof(f89,plain,
ilf_type(sk0_4,binary_relation_type),
inference(cnf_transformation,[status(esa)],[f88]) ).
fof(f90,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f100,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( subset(B,C)
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f101,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f100]) ).
fof(f102,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ( ilf_type(sk0_6(C,B),set_type)
& member(sk0_6(C,B),B)
& ~ member(sk0_6(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f101]) ).
fof(f105,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1)
| member(sk0_6(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f102]) ).
fof(f106,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1)
| ~ member(sk0_6(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f102]) ).
fof(f111,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f112,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f127,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(cnf_transformation,[status(esa)],[f127]) ).
fof(f129,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( member(B,power_set(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f130,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f129]) ).
fof(f131,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ( ilf_type(sk0_11(C,B),set_type)
& member(sk0_11(C,B),B)
& ~ member(sk0_11(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f136,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f137,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[status(esa)],[f136]) ).
fof(f139,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f140,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(B,member_type(C))
| member(B,C) )
& ( ilf_type(B,member_type(C))
| ~ member(B,C) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f139]) ).
fof(f141,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f140]) ).
fof(f154,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(cnf_transformation,[status(esa)],[f154]) ).
fof(f156,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(domain(X0,X1,X2),subset_type(X0)) ),
inference(cnf_transformation,[status(esa)],[f156]) ).
fof(f158,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(cnf_transformation,[status(esa)],[f158]) ).
fof(f160,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(range(B,C,D),subset_type(C)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f35]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(cnf_transformation,[status(esa)],[f160]) ).
fof(f166,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f167,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,identity_relation_of_type(B))
& ( compose(C,identity_relation_of(B)) != C
| compose(identity_relation_of(B),C) != C ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f40]) ).
fof(f168,plain,
( ilf_type(sk0_14,set_type)
& ilf_type(sk0_15,identity_relation_of_type(sk0_14))
& ( compose(sk0_15,identity_relation_of(sk0_14)) != sk0_15
| compose(identity_relation_of(sk0_14),sk0_15) != sk0_15 ) ),
inference(skolemization,[status(esa)],[f167]) ).
fof(f170,plain,
ilf_type(sk0_15,identity_relation_of_type(sk0_14)),
inference(cnf_transformation,[status(esa)],[f168]) ).
fof(f171,plain,
( compose(sk0_15,identity_relation_of(sk0_14)) != sk0_15
| compose(identity_relation_of(sk0_14),sk0_15) != sk0_15 ),
inference(cnf_transformation,[status(esa)],[f168]) ).
fof(f172,plain,
( spl0_0
<=> compose(sk0_15,identity_relation_of(sk0_14)) = sk0_15 ),
introduced(split_symbol_definition) ).
fof(f175,plain,
( spl0_1
<=> compose(identity_relation_of(sk0_14),sk0_15) = sk0_15 ),
introduced(split_symbol_definition) ).
fof(f178,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f171,f172,f175]) ).
fof(f181,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f87]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ilf_type(range(X2,X0,X1),subset_type(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f161,f166]) ).
fof(f189,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f166]) ).
fof(f190,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| range(X2,X0,X1) = range_of(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f159,f166]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f166]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ilf_type(domain(X2,X0,X1),subset_type(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f157,f166]) ).
fof(f193,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f166]) ).
fof(f194,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| domain(X2,X0,X1) = domain_of(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f155,f166]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f166]) ).
fof(f201,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f141,f166]) ).
fof(f202,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f166]) ).
fof(f203,plain,
! [X0] : ~ empty(power_set(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f137,f166]) ).
fof(f208,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f132,f166]) ).
fof(f209,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f166]) ).
fof(f210,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| relation_like(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f128,f166]) ).
fof(f211,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f166]) ).
fof(f220,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[f113,f166]) ).
fof(f221,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f166]) ).
fof(f223,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| subset(X1,X0)
| ~ member(sk0_6(X0,X1),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f106,f166]) ).
fof(f224,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_6(X1,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f166]) ).
fof(f225,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| subset(X1,X0)
| member(sk0_6(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f105,f166]) ).
fof(f226,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_6(X1,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f166]) ).
fof(f231,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ilf_type(X1,subset_type(cross_product(X2,X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[f92,f166]) ).
fof(f232,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f166]) ).
fof(f235,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f181,f166]) ).
fof(f240,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,identity_relation_of_type(X1))
| ilf_type(X0,relation_type(X1,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f63,f166]) ).
fof(f241,plain,
! [X0,X1] :
( ~ ilf_type(X0,identity_relation_of_type(X1))
| ilf_type(X0,relation_type(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f166]) ).
fof(f242,plain,
! [X0] : ilf_type(identity_relation_of(X0),binary_relation_type),
inference(backward_subsumption_resolution,[status(thm)],[f60,f166]) ).
fof(f255,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ subset(range_of(X0),X1)
| compose(X0,identity_relation_of(X1)) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[f44,f166]) ).
fof(f256,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ subset(domain_of(X0),X1)
| compose(identity_relation_of(X1),X0) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f166]) ).
fof(f303,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| empty(power_set(X1))
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f221,f202]) ).
fof(f304,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f203]) ).
fof(f308,plain,
! [X0,X1] :
( range(X0,X0,X1) = range_of(X1)
| ~ ilf_type(X1,identity_relation_of_type(X0)) ),
inference(resolution,[status(thm)],[f191,f241]) ).
fof(f321,plain,
range(sk0_14,sk0_14,sk0_15) = range_of(sk0_15),
inference(resolution,[status(thm)],[f308,f170]) ).
fof(f322,plain,
( spl0_2
<=> ilf_type(sk0_15,relation_type(sk0_14,sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f323,plain,
( ilf_type(sk0_15,relation_type(sk0_14,sk0_14))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f324,plain,
( ~ ilf_type(sk0_15,relation_type(sk0_14,sk0_14))
| spl0_2 ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( spl0_3
<=> ilf_type(range_of(sk0_15),subset_type(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f326,plain,
( ilf_type(range_of(sk0_15),subset_type(sk0_14))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( ~ ilf_type(sk0_15,relation_type(sk0_14,sk0_14))
| ilf_type(range_of(sk0_15),subset_type(sk0_14)) ),
inference(paramodulation,[status(thm)],[f321,f189]) ).
fof(f329,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f328,f322,f325]) ).
fof(f330,plain,
( ~ ilf_type(sk0_15,identity_relation_of_type(sk0_14))
| spl0_2 ),
inference(resolution,[status(thm)],[f324,f241]) ).
fof(f331,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f170]) ).
fof(f332,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f331]) ).
fof(f339,plain,
( domain(sk0_14,sk0_14,sk0_15) = domain_of(sk0_15)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f195,f323]) ).
fof(f341,plain,
( spl0_4
<=> ilf_type(domain_of(sk0_15),subset_type(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f342,plain,
( ilf_type(domain_of(sk0_15),subset_type(sk0_14))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,plain,
( ~ ilf_type(sk0_15,relation_type(sk0_14,sk0_14))
| ilf_type(domain_of(sk0_15),subset_type(sk0_14))
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f339,f193]) ).
fof(f345,plain,
( ~ spl0_2
| spl0_4 ),
inference(split_clause,[status(thm)],[f344,f322,f341]) ).
fof(f348,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(resolution,[status(thm)],[f209,f166]) ).
fof(f375,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ member(sk0_6(X1,X2),X0)
| subset(X2,X1) ),
inference(resolution,[status(thm)],[f348,f224]) ).
fof(f378,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[status(thm)],[f232,f211]) ).
fof(f382,plain,
( relation_like(sk0_15)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f378,f323]) ).
fof(f449,plain,
( ilf_type(sk0_15,binary_relation_type)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f382,f235]) ).
fof(f510,plain,
( spl0_12
<=> ilf_type(sk0_15,binary_relation_type) ),
introduced(split_symbol_definition) ).
fof(f512,plain,
( ~ ilf_type(sk0_15,binary_relation_type)
| spl0_12 ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f528,plain,
( $false
| ~ spl0_2
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f449]) ).
fof(f529,plain,
( ~ spl0_2
| spl0_12 ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f677,plain,
( spl0_21
<=> ilf_type(sk0_4,binary_relation_type) ),
introduced(split_symbol_definition) ).
fof(f679,plain,
( ~ ilf_type(sk0_4,binary_relation_type)
| spl0_21 ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,plain,
( spl0_22
<=> ilf_type(identity_relation_of(range_of(sk0_4)),binary_relation_type) ),
introduced(split_symbol_definition) ).
fof(f682,plain,
( ~ ilf_type(identity_relation_of(range_of(sk0_4)),binary_relation_type)
| spl0_22 ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f700,plain,
( $false
| spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f682,f242]) ).
fof(f701,plain,
spl0_22,
inference(contradiction_clause,[status(thm)],[f700]) ).
fof(f702,plain,
( $false
| spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f679,f89]) ).
fof(f703,plain,
spl0_21,
inference(contradiction_clause,[status(thm)],[f702]) ).
fof(f720,plain,
( spl0_26
<=> ilf_type(identity_relation_of(domain_of(sk0_4)),binary_relation_type) ),
introduced(split_symbol_definition) ).
fof(f722,plain,
( ~ ilf_type(identity_relation_of(domain_of(sk0_4)),binary_relation_type)
| spl0_26 ),
inference(component_clause,[status(thm)],[f720]) ).
fof(f740,plain,
( $false
| spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f722,f242]) ).
fof(f741,plain,
spl0_26,
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f785,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f375,f226]) ).
fof(f786,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f785]) ).
fof(f797,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[f786,f304]) ).
fof(f967,plain,
( spl0_36
<=> ilf_type(identity_relation_of(domain_of(sk0_15)),binary_relation_type) ),
introduced(split_symbol_definition) ).
fof(f969,plain,
( ~ ilf_type(identity_relation_of(domain_of(sk0_15)),binary_relation_type)
| spl0_36 ),
inference(component_clause,[status(thm)],[f967]) ).
fof(f989,plain,
( $false
| spl0_36 ),
inference(forward_subsumption_resolution,[status(thm)],[f969,f242]) ).
fof(f990,plain,
spl0_36,
inference(contradiction_clause,[status(thm)],[f989]) ).
fof(f992,plain,
( spl0_40
<=> ilf_type(identity_relation_of(range_of(sk0_15)),binary_relation_type) ),
introduced(split_symbol_definition) ).
fof(f994,plain,
( ~ ilf_type(identity_relation_of(range_of(sk0_15)),binary_relation_type)
| spl0_40 ),
inference(component_clause,[status(thm)],[f992]) ).
fof(f1014,plain,
( $false
| spl0_40 ),
inference(forward_subsumption_resolution,[status(thm)],[f994,f242]) ).
fof(f1015,plain,
spl0_40,
inference(contradiction_clause,[status(thm)],[f1014]) ).
fof(f1056,plain,
( subset(domain_of(sk0_15),sk0_14)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f797,f342]) ).
fof(f1059,plain,
( subset(range_of(sk0_15),sk0_14)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f797,f326]) ).
fof(f1314,plain,
( ~ ilf_type(sk0_15,binary_relation_type)
| compose(identity_relation_of(sk0_14),sk0_15) = sk0_15
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f1056,f256]) ).
fof(f1315,plain,
( ~ spl0_12
| spl0_1
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f1314,f510,f175,f341]) ).
fof(f1317,plain,
( ~ ilf_type(sk0_15,binary_relation_type)
| compose(sk0_15,identity_relation_of(sk0_14)) = sk0_15
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f1059,f255]) ).
fof(f1318,plain,
( ~ spl0_12
| spl0_0
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f1317,f510,f172,f325]) ).
fof(f1320,plain,
$false,
inference(sat_refutation,[status(thm)],[f178,f329,f332,f345,f529,f701,f703,f741,f990,f1015,f1315,f1318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET678+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.36 % Computer : n029.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Apr 29 22:07:49 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.38 % Drodi V3.6.0
% 1.41/0.60 % Refutation found
% 1.41/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.41/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.41/0.61 % Elapsed time: 0.247577 seconds
% 1.41/0.61 % CPU time: 1.805419 seconds
% 1.41/0.61 % Total memory used: 84.085 MB
% 1.41/0.61 % Net memory used: 83.256 MB
%------------------------------------------------------------------------------